In a diagram, ∠A and ∠B are vertical angles, and ∠B is a complementary angle with ∠C . If m∠A=22° , write an equation that you can use to solve for m∠C .(2 points)
Since angle A and angle B are vertical angles, they are congruent. Therefore, m∠A = m∠B.
Since angle B is a complementary angle with angle C, their sum is 90 degrees. Therefore, m∠B + m∠C = 90.
Substituting m∠A = 22° for m∠B in the second equation, we have:
22 + m∠C = 90.
So, the equation we can use to solve for m∠C is:
m∠C = 90 - 22 = 68.